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187370953756
@187370953756
July 2022
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lim 2√х+3−4/х−1 (x+3 - под корнем, 2√х+3−4 - числитель, х-1 - знаменатель)
x->1
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kirichekov
Verified answer
Lim((2√(x+3)-4)/(x-1))=(2*√(1+3)-4)/(1-1)=0/0
x->1
lim((2√(x+3)-4)/(x-1))=
x->1
=lim((2√(x+3)-4)*(2√(x+3)+4))/((x-1)*(2√(x+3)+4))=
x->1
=lim((2√(x+3))²-4²)/((x-1)*(2√(x+3)+4)=
x->1
=lim(4*(x+3)-16)/((x-1)*(2√(x+3)+4))=
x->1
=lim(4x-4)/((x-1)*(2√(x+3)+4))=
x->1
=lim(4*(x-1))/((x-1)*(2(√(x+1)+2))=
x->1
=lim4/2(√(x+3)+2)=lim2/(√(x+3)+2)=2/(√(1+3)+2)=2/4=
1/2=0,5
x->1
1 votes
Thanks 1
kirichekov
скобок много. запишите числитель и знаменатель, их будет меньше
187370953756
Спасибо.
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Answers & Comments
Verified answer
Lim((2√(x+3)-4)/(x-1))=(2*√(1+3)-4)/(1-1)=0/0x->1
lim((2√(x+3)-4)/(x-1))=
x->1
=lim((2√(x+3)-4)*(2√(x+3)+4))/((x-1)*(2√(x+3)+4))=
x->1
=lim((2√(x+3))²-4²)/((x-1)*(2√(x+3)+4)=
x->1
=lim(4*(x+3)-16)/((x-1)*(2√(x+3)+4))=
x->1
=lim(4x-4)/((x-1)*(2√(x+3)+4))=
x->1
=lim(4*(x-1))/((x-1)*(2(√(x+1)+2))=
x->1
=lim4/2(√(x+3)+2)=lim2/(√(x+3)+2)=2/(√(1+3)+2)=2/4=1/2=0,5
x->1